Method for target-oriented reverse time migration for prestack depth imaging

ABSTRACT

A method and system for target-oriented reverse time migration for prestack depth imaging. One embodiment of the present invention includes determining an acquisition area within an earth model and also determining a reference surface near a target in the subsurface region of interest. The embodiment includes exciting wavefields from the reference surface and propagating the excited wavefields through the earth model. The embodiment additionally includes recording the wavefields at receiver locations in the acquisition area and at the target and synthesizing wavefields along the reference surface to reconstruct Green&#39;s functions which relate the receiver locations in the acquisition area to the target. The embodiment includes utilizing the Green&#39;s functions and prestack seismic data to determine subsurface characteristics of the subsurface region.

TECHNICAL FIELD

The present invention relates generally to geophysical prospecting usingseismic data, and in particular to a method of migration of seismic dataand inversion for subsurface property distributions.

BACKGROUND OF THE INVENTION

Rigorous solutions of wave equation are highly accurate in simulatingwave propagation through complex subsurface regions. Downwardcontinuation methods based on the one-way wave equation are well knownfor their computational efficiency and accuracy in handling multi-pathevents. Reverse-time migration (RTM) offers additional advantages overone-way imaging by removing the dip limitation and therefore is capableof handling wave propagation in any direction. Consequently a morecomplete set of waves (for example, prismatic waves, overturning wavesand potentially multiples) can be used constructively for imagingchallenging subsurface structures, such as steeply dipping oroverhanging salt flanks. Although becoming increasingly affordable, RTMis generally considered more computationally intensive than one-waydownward continuation methods.

The high computational cost of RTM arises from solving the two-waywavefield propagation. For example, the source wavefield is propagatedover time and saved to an electronic storage medium. As a result, RTMrequires a significant storage space for reverse-time access of 3Dsource wavefields unless wavefield storage is traded with increasedcomputation time. In RTM, in addition to the forward wavefieldpropagation, the seismic data are back extrapolated and correlated withthe source wavefield. The runtime cost of RTM is thus approximatelytwice that of forward full-wavefield modeling.

Several prior art methods have been proposed to make RTM more efficientfor practical applications in recent years. One prior art method showsthat RTM is equivalent to Generalized Diffraction Stack Migration (GDM).A reduced version of GDM, called wavefront wave-equation migration, usesonly first-arrival information to back-propagate arrivals. Byintroducing a square-root operator, another prior art method shows thatthe two-way wave equation can be formulated as a first-order partialdifferential equation (PDE) for cost-effective implementation. Yetanother prior art method suggests target-oriented reverse time datuming(RTD) by extrapolating wavefields to a subsalt artificial datum using afinite-difference solver. Below the datum, a less intensive imagingmethod such as Kirchhoff migration can be used. Most recently, anotherprior art method showed test examples of target-oriented RTD. There,however, still exists a need for methods which perform RTM inless-costly computational ways.

SUMMARY OF THE INVENTION

A method for target-oriented reverse time migration for prestack depthimaging and inversion is provided. The method includes acquiringprestack seismic data for a subsurface region, and determining an earthmodel for the subsurface region. The method further includes determiningan acquisition area within the earth model and also determining areference surface near a target within the earth model. The method alsoincludes exciting wavefields from the reference surface and propagatingthe excited wavefields through the earth model. The method additionallyincludes recording the wavefields at receiver locations in theacquisition area and at the target, and synthesizing wavefields alongthe reference surface to reconstruct Green's functions or otherequivalent transfer functions which relate the receiver locations in theacquisition area to the target. The method includes utilizing theGreen's functions and prestack seismic data to determine subsurfacecharacteristics of the subsurface region.

It can be appreciated by one skilled in the art that point sources orplane wave sources can be used to excite wavefields from the referencesurface.

It can also be appreciated that the Green's functions can be utilized toconstruct images at the target which represent the subsurface at thetarget and the images can also be used in an inversion process todetermine subsurface properties.

The present invention does not require intermediate data datuming anddirectly applies two-way scattered Green's functions for imaging targetareas. The Green's functions relating the acquisition area and theimaging target are retained and separated from seismic data untilapplying the imaging condition. Such a separation of Green's functionsand data provides analysis flexibility. The target-oriented approachallows for the ability to focus on critically important areas whileattaining the capabilities of two-way imaging from RTM. The presentinvention is applicable to both 2D and 3D data sets and geometries.

It should also be appreciated by one skilled in the art that the presentinvention is intended to be used with a system which includes, ingeneral, an electronic configuration including at least one processor,at least one memory device for storing program code or other data, avideo monitor or other display device (i.e., a liquid crystal display)and at least one input device. The processor is preferably amicroprocessor or microcontroller-based platform which is capable ofdisplaying images and processing complex mathematical algorithms. Thememory device can include random access memory (RAM) for storing eventor other data generated or used during a particular process associatedwith the present invention. The memory device can also include read onlymemory (ROM) for storing the program code for the controls and processesof the present invention.

One embodiment of the present invention includes a system configured toperform target-oriented reverse time migration for prestack depthimaging. The system includes a data storage device having computerreadable data including prestack seismic data and an earth model for asubsurface region, and a processor, configured and arranged to executemachine executable instructions stored in a processor accessible memoryfor performing a method. The method includes determining an acquisitionarea within the earth model and determining a reference surface near atarget in the subsurface region of interest, and exciting wavefieldsfrom the reference surface and propagating the excited wavefieldsthrough the earth model. The method further includes recording thewavefields at receiver locations in the acquisition area and at thetarget, and synthesizing wavefields along the reference surface toreconstruct Green's functions which relate the receiver locations in theacquisition area to the target. The method includes utilizing theGreen's functions and prestack seismic data to determine subsurfacecharacteristics of the subsurface region.

Embodiments of the present invention can also be used to providelocalized imaging update following model change and/or provide localizedmodel building or updating by generating gathers at target locations.Embodiments of the present invention can also be utilized tointeractively test uncertainties in structural imaging given errors inthe velocity/anisotropy models. In yet other embodiments, the presentinvention can be used for localized waveform inversion.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other objects, features and advantages of the presentinvention will become better understood with regard to the followingdescription, pending claims and accompanying drawings where:

FIG. 1 illustrates a flowchart of one embodiment of the presentinvention.

FIG. 2 illustrates one embodiment of the present invention wherein thereference surface is shown in reference to an example of surface used ina prior art full-volume method.

FIG. 3 illustrates a flowchart of one embodiment of the presentinvention.

FIGS. 4A to 4D illustrate the images for one embodiment of the presentinvention and a prior art full-volume method for a single reflector.

FIGS. 5A to 5D illustrate the results of different sampling densities onthe reference surface for one embodiment of the present invention.

FIG. 6 illustrates the acquisition geometry for one embodiment of thepresent invention and a prior art method for a vertical reflector.

FIGS. 7A and 7B illustrate the images for one embodiment of the presentinvention and a prior art method for a vertical reflector.

FIGS. 8A to 8D illustrate the results of different sampling densities onthe reference surface for one embodiment of the present invention.

FIG. 9 illustrates the imaging target area based on a prior artfull-volume method.

FIGS. 10A and 10B illustrate the images for one embodiment of thepresent invention and a prior art full-volume method for the target areainvolving an overhanging salt flank.

FIGS. 11A and 11B illustrate the illumination intensity for oneembodiment of the present invention and a prior art full-volume methodfor the target area.

FIGS. 12A to 12D illustrate the velocity model and images for oneembodiment of the present invention and a prior art full-volume methodfor a deepwater complex structure

FIG. 13 schematically illustrates an example of a system for performingthe present invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention improves the computational efficiency of RTM byfocusing on target areas. Computational savings is achieved throughlimiting Green's functions related to target areas instead of over theentire volume of an earth model.

FIG. 1 illustrates one embodiment of the present invention for acomputer-implemented method for target-oriented reverse time migrationfor prestack depth imaging 10. The method includes acquiring prestackseismic data for a subsurface region 12 and determining an earth modelfor the subsurface region 14. The method further includes determining anacquisition area within the earth model and determining a referencesurface near a target within the earth model 16, and exciting wavefieldsfrom the reference surface and propagating the excited wavefieldsthrough the earth model 18. The method also includes recording thewavefields at receiver locations in the acquisition area and at thetarget 20, and synthesizing wavefields along the reference surface toreconstruct Green's functions or other equivalent transfer functionswhich relate the receiver locations in the acquisition area to thetarget 22. The method includes utilizing the Green's functions todetermine subsurface characteristics of the subsurface region 24.

In one prior art method, Schuster's formulation (2002) of migration inthe frequency domain, the prestack depth imaging condition for asubsurface image point, x, can be described as follows:

${I(x)} = {\sum\limits_{w}{\sum\limits_{s}{\sum\limits_{r}{{G\left( {{x❘s},w} \right)}^{*}\left\{ {{G\left( {{x❘r},w} \right)}^{*}{D\left( {s,r,w} \right)}} \right\}}}}}$where I(x) is the image at subsurface point x; D(s,r,w) are shot gathersassociated with source location s and receivers r; G(x|r,w) and G(x|s,w)represent the Green's functions from the receivers and the source,respectively, to the image point; and * denotes the complex conjugate.The conjugate of the Green's function multiplying seismic data in thefrequency domain is equivalent to the cross correlation of the two termsin the time domain. The summation works in the order of receivers, shotsand finally frequencies. The above imaging condition can be furthercompensated by wavefield illumination.

A key challenge in the above-described prior art formulation is tocompute the Green's functions from receiver locations to image pointsboth accurately and efficiently. To save computational cost, the presentinvention utilizes the Green's functions which are related only to imagepoints within a target volume. However, it can be too costly to computeGreen's functions G(x|r,w) directly, given the large number of imagepoints even in a target zone.

One embodiment of the present invention breaks down the process into twosteps. First, the Green's functions, G(d|r,w), are calculated fromreceiver locations to an artificial datum above the target zone. Second,the Green's functions, G(x|d,w), are calculated from the datum down tothe image points. By summing over the datum through stationary phaseapproximation, the Green's functions, G(x|r,w), can be reconstructedfrom its two breakdown components, G(d|r,w) and G(x|d,w), as follows:

${G\left( {{x❘r},w} \right)} \approx {\sum\limits_{datum}{{G\left( {{d❘r},w} \right)}{G\left( {{x❘d},w} \right)}}}$

In certain embodiments of the present invention, the Green's functionsare computed by using a two-way finite-difference solver. It should beappreciated by one skilled in the art that other forms of modeling canalso be used depending on the complexity of medium properties. Thesummation over the area of datum ensures that only stationary-phasecontributions stand out. To meet the criterion of stationary phaseapproximation, the spatial sampling over the artificial datum needs tobe fine enough, and the aperture coverage needs to be wide enough overthe target. It will be appreciated by one skilled in the art that theartificial datum or reference surface around the target area can be ofdifferent shapes and is not limited to a flat surface.

The gain in computational efficiency in the target-oriented approach ofthe present invention is two-fold. First, the number of samples over anartificial datum is significantly fewer than that of shot gathers overthe surface. FIG. 2 illustrates this computational savings for oneembodiment of the present invention where point sources have been used.For prior art methods where the full volume 34 RTM is being determinedthe number of point sources 28 utilized in RTM is significantly higherthan the point sources 30 utilized by the present invention. The presentinvention utilizes a datum or reference surface 32 that is smaller thanthe surface 26 for traditional RTM, thus, the present invention is ableto use less point sources 30 than prior art RTM. In general, the datumfor splitting Green's functions is selected close to a spatially limitedtarget zone. In addition, interpolation of coarse samples over the datummay provide further savings. Second, the decomposed Green's functionsover and under the datum can be computed simultaneously. On thecontrary, wave propagation in traditional RTM is computed twice: thefirst for the source wavefield and the second for the receiverwavefield.

FIG. 3 shows a method 36 of one embodiment of the present invention forthe target-oriented reverse-time migration. As can be appreciated, thisparticular embodiment can be readily implemented parallel in frequencyon Linux clusters. The Green's functions are computed by FiniteDifference (FD) modeling 38. The method then performs a Fast FourierTransform (FFT) on the computed Green's functions 40. The acquisitionsurface to target Green's functions are reconstructed 42. In thisembodiment, in concurrence with this step 42, a FFT is performed on theinput seismic data 46 and is used as inputs along with the reconstructedGreen's functions 42 to provide imaging conditions 48. The method thenconstructs images of the target zone 50 which can be used to determinethe subsurface characteristics of the subsurface region.

FIGS. 4A to 4D illustrate one embodiment of the present invention, wherea strong velocity contrast 52 lies at 3 km in depth. FIG. 4A is avelocity model of the subsurface region of interest utilized for thisembodiment. FIG. 4B is the single shot gather with the source at thecenter. FIG. 4C is the target-oriented RTM imaging results, and FIG. 4Dis the prior art full-volume RTM imaging results for comparison. In thisembodiment both images are from a single shot gather. An artificialdatum or reference surface 54 for reconstructing the target Green'sfunction is 1 km above the target area 56. The reference surface 54 issampled at a 50 m spacing to generate Green's functions by afinite-difference solver. By applying target-oriented imaging conditionto a single shot gather, the velocity contrast 52 is imaged as a flatevent 60 at the correct position.

Proper sampling over the reference surface is important to hold thestationary phase approximation valid. FIGS. 5A to 5D illustrate thatwith increasing sampling density over the reference surface, thereconstructed Green's function approaches the correct answer. FIG. 5A isagain a velocity model for the subsurface of interest. FIG. 5B is theimaging results of this embodiment with the reference surface orartificial datum sampled at 500 m apart. FIG. 5C is the imaging resultsof this embodiment with the reference surface sampled at 50 m apart.FIG. 5D is the prior art full-volume RTM image for comparison with theimaging results of the present invention. In this embodiment, there areghost events 62 due to the presence of the reference surface and two-waywave propagation. However, the ghost events 62 are usually out of phaseand do not contribute to final images. Some edge effects 64 are alsovisible in FIG. 5C. They can be tapered to minimize adverse effects onimages.

FIGS. 6, 7A and 7B illustrate another embodiment of the presentinvention where the imaging target is a vertical reflector 66. FIG. 6illustrates a velocity model for the subsurface region of interest andshows the reference surface 68. FIG. 7A illustrates an image obtainedwith this embodiment of the present invention for the target-orientedimaging. FIG. 7B illustrates an image utilizing the prior art method offull-volume of RTM. The velocity throughout the whole region is aconstant at 2000 m/s. One skilled in the art would appreciate that sucha velocity distribution would make it impossible to image the verticalreflector using one-way imaging. As shown in FIG. 7A, the verticalreflector 70 is well focused and correctly positioned. This indicatesthat target-oriented imaging of the present invention is capable ofutilizing multi-bouncing events (or prism waves) for imaging subsurfaceregions.

FIGS. 8A to 8D illustrate the results of different sampling densities onthe reference surface for one embodiment of the present invention. Inthis example, the sampling rate varies from 10 m to 80 m. Sampling rateclose to the dominant wavelength (40 m) still retains accurate imagingwith minimal artifacts.

Another embodiment of the present invention is illustrated in FIGS. 9,10A and 10B. FIG. 9 illustrates a target imaging area highlighted by abox 72 for the subsurface region of interest. The reference surface 74is set at 1 km left of the target 72 and sampled at a 80 m spacing togenerate Green's functions left and right of the datum 74. FIG. 10Aillustrates the target-oriented RTM image of the present invention, andfor comparison FIG. 10B illustrates the prior art full-volume RTMimaging. The images in these figures are based on a single shot gather.As shown in FIG. 10A, the overhanging salt flank is recovered bytarget-oriented RTM. FIGS. 11A and 11B compare the illuminationintensity over the imaging region of interest. The illuminationintensity is an autocorrelation of the reconstructed Green's functionswhich relate the acquisition surface to the target.

It should be appreciated that the present invention can also utilizemultiple shot gathers. FIGS. 12A to 12D illustrate an embodimentutilizing multiple shot gathers for a deepwater complex structure. FIG.12A illustrates a velocity model for the subsurface region of interest.The dashed line indicates the reference surface 76 for the targetimaging 78 of the present invention. FIG. 12B is an enhanced view of thetarget 78 in the velocity model. FIG. 12C illustrates thetarget-oriented RTM image of the present invention, and for comparisonFIG. 12D illustrates the prior art full-volume RTM imaging. The numberof shots utilized with the reference surface for this embodiment is 188with a 160 foot spacing. The seismic data utilized in this embodimentconsists of 435 shot gathers recorded on surface. The reference surfaceis selected above a rugose part of top-of-salt 80 and intersects asteeply dipping salt flank 82. The target-oriented images of the presentinvention and the full-volume images are comparable in structuraldelineation of the complex deepwater structure including the steeplydipping and overhanging salt flanks.

It will be appreciated by one skilled in the art that the presentinvention can be applied to 3D.

An example of a system for performing the present invention isschematically illustrated in FIG. 13. A system 84 includes a datastorage device or memory 86. The stored data may be made available to aprocessor 88, such as a programmable general purpose computer. Theprocessor 88 may include interface components such as a display 90 and agraphical user interface (GUI) 92. The GUI 92 may be used both todisplay data and processed data products and to allow the user to selectamong options for implementing aspects of the method. Data may betransferred to the system 84 via a bus 94 either directly from a dataacquisition device, or from an intermediate storage or processingfacility (not shown).

While in the foregoing specification this invention has been describedin relation to certain preferred embodiments thereof, and many detailshave been set forth for purpose of illustration, it will be apparent tothose skilled in the art that the invention is susceptible to alterationand that certain other details described herein can vary considerablywithout departing from the basic principles of the invention.

1. A computer-implemented method for target-oriented reverse time migration for prestack depth imaging, the method including: acquiring prestack seismic data for a subsurface region; determining, via a computer, an earth model for the subsurface region; determining, via a computer, an acquisition area within the earth model; determining, via a computer, a reference surface near a target within the earth model; exciting, via a computer, wavefields from the reference surface; propagating, via a computer, the excited wavefields through the earth model; recording, via a computer, the wavefields at receiver locations in the acquisition area and at the target; synthesizing, via a computer, wavefields along the reference surface to reconstruct Green's functions which relate the receiver locations in the acquisition area to the target; and utilizing, via a computer, the Green's functions and prestack seismic data to determine subsurface characteristics of the subsurface region.
 2. The method of claim 1 wherein either point sources or plane waves is utilized to excite wavefields from the reference surface.
 3. The method of claim 1 wherein the subsurface characteristics of the subsurface region is utilized to construct images at the target which represent the subsurface region at the target.
 4. The method of claim 1 wherein the subsurface characteristics of the subsurface region is utilized in an inversion to determine subsurface properties of the subsurface region at the target.
 5. The method of claim 1 wherein the prestack seismic data is either 2D or 3D.
 6. A system configured to perform target-oriented reverse time migration for prestack depth imaging, the system comprising: a data storage device having computer readable data including prestack seismic data and an earth model for a subsurface region; a processor, configured and arranged to execute machine executable instructions stored in a processor accessible memory for performing a method comprising: determining an acquisition area within the earth model; determining a reference surface near a target in the subsurface region of interest; exciting wavefields from the reference surface; propagating the excited wavefields through the earth model; recording the wavefields at receiver locations in the acquisition area and at the target; synthesizing wavefields along the reference surface to reconstruct Green's functions which relate the receiver locations in the acquisition area to the target; and utilizing the Green's functions and the prestack seismic data to determine subsurface characteristics of the subsurface region.
 7. A system as in claim 6, further comprising a display, configured and arranged to display at least one image which represents the subsurface region at the target, where in the image was constructed utilizing the subsurface characteristics of the subsurface region.
 8. The system of claim 6 wherein either point sources or plane waves is utilized to excite wavefields from the reference surface.
 9. The system of claim 6 wherein the subsurface characteristics of the subsurface region can used in inversion to determine subsurface properties of the subsurface region at the target.
 10. The system of claim 6 wherein the prestack seismic data is either 2D or 3D. 